The first thing I would advise to be done is to check your laptop with an external monitor to make sure that it is not the video chip that went bad. So connect your laptop to an external monitor and see if you get a picture (you might have to press the fn and one of the f1 , f2 , f3 etc....keys together to switch the output to an external display , If you get a picture on the external monitor you know it is not the motherboard , (whew, was getting scared already). If you don't get a picture on the external monitor make sure it is plugged in correctly and that you pressed the correct keys to have the output signal go to the external monitor. If you are sure you did all of the above steps correctly , then shut off the computer and try pressing down on the keyboard while powering up the laptop and see if you get an image. Sometimes if a computer has a loose connection between the GPU (Graphical Processing Unit) and the motherboard it will result in no video or flaky video , so try pressing down on the keyboard while powering on and try see if you get video. If you get a video output then you will know that it is a flaky video chip and that will have to be fixed.
Now back to if you got a picture on an external display. Once you got a picture on the external monitor and established that it is not the video chip or motherboard you will have to try to determine if it is the lcd screen itself or if it is the inverter. The inverter is a small electronic board that controls the voltage that is sent to the backlight (the light bulb of the laptop screen) of the lcd screen. If the inverter breaks or dies then no voltage gets to the backlight resulting in no video output signal to the display. In my experience working as a technician for www.nylaptopparts.com I see that most of the times it is the inverter that is the problem and that is a pretty easy fix , you just have to get the correct inverter that supplies the right amount of voltage and you will be back in business. But in some instances it is the backlight (light bulb) that went , and to repair this is more difficult and more time consuming. One way to see if it is the inverter , is to test the two prongs of the inverter with a voltage meter and see if they are giving off the correct voltage (please read up more on this method , as inverters have high voltage output , so you have to know what you are doing , so I strongly advise to read up on this more prior to doing it. Another simpler way is to shine a flashlight on the lcd , if you see a faint image then in most cases it is the backlight that needs to be replaced. If you don't see an image even when shining the flashlight then it is most likely the inverter and it should be an easy fix.
On a last note if you determined that it is the backlight that is faulty , although it is fixable it requires more time and experience then just replacing the inverter , and if one is not experienced he/she can damage the lcd screen itself as well , so generally if the backlight is faulty either have a laptop repair shop replace the backlight , but only one who has experience. Or another option is to buy a new lcd panel and install it either yourself or proffesionally. Generally it is not very difficult to replace a lcd panel but there are some models that are more difficult so try to ask a laptop repair shop about your specific model